You have to write a Java program, comparing the accuracy of numerical integration techniques:

• start by creating a class IntegralTst
• import ptolemy.plot*.
• in your class:
  • create a double method fun(double x), returning Exp(x)
  • create a double method trapWt(int i, int N) returning a weight of i-th integration point out of N in Trapezoid method
  • create a double method simpWt(int i, int N) returning a weight of i-th integration point out N in Simpson's method
  • create a double method intTrap(double a, double b, int N), calculating the integral of fun(x), a<=x<=b using N points with trapezoid method.
  • create a double method intSimp(double a, double b, int N), calculating the integral of fun(x), a<=x<=b using N points with Simpson's method.
• in your main method
  • create a double variables trap, simp, exact
  • initialize exact with exp(5.)-1.;
  • create an integer variable n
  • define Plot variable myPlot
  • start for loop over the variable n with the following parameters:
    • initial value =1,
    • final value=1001
    • loop step=50
  • in each iteration of your loop:
    • calculate trap=intTrap(0,5,n);
    • calculate simp=intSimp(0,5,n);
    • add a point (i, log(abs(trap-exact))) to the first (0) set of myPlot; connect the graph points; log scale will help you distinguish between near-zero values
    • add a point (i, log(abs(simp-exact))) to the second (1) set of myPlot; connect the graph points
  • display myPlot, print it (on paper)
  • add a comment to your code about the relative accuracy of Trapezoidal and Simpson's techniques.
• submit: printed code and the printed graph(s)

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